• Korean Journal of Logic
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• v.22 no.3
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• pp.397-415
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• 2019

This paper deals with the pretabular property of some fuzzy logics. For this, we first introduce the involutive idempotent uninorm logics IdIUL and IUML and examine the relationship between IdIUL and the another well-known system $RM^T$. Next, we show that IUML is pretabular, whereas IdIUL is not.

• Korean Journal of Logic
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• v.14 no.1
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• pp.55-76
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• 2011

Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

• Korean Journal of Logic
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• v.11 no.1
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• pp.131-156
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• 2008

This paper first investigates several uninorm logics (introduced by Metcalfe and Montagna in [8]) as fuzzy-relevance logics. We first show that the uninorm logic UL and its extensions IUL, UML, and IUML are fuzzy-relevant; fuzzy in Cintula's sense, i.e., the logic L is complete with respect to linearly ordered L-matrices; and relevant in the weak sense that ${\Phi}{\rightarrow}{\Psi}$ is a theorem only if either (i) $\Phi$ and $\Psi$ share a sentential variable or constant, or (ii) both $\sim\Phi$ and $\Psi$ are theorems. We next expand these systems to those with $\triangle$.